Many Kenyans believe the question is insensitive, coming 18 months after more than 1,000 people were killed in ethnic violence after an election.
Ministers say the question is needed to help the authorities plan better.
Critics say the census will be misused by politicians and could damage efforts to heal rifts between communities.
The final results of the last census in 1999 were never released.
In the past, there have been accusations that some communities have tried to rig the population numbers to get an undue advantage when it comes to the sharing of resources.
The BBC's Will Ross in Nairobi says ethnic divisions are deeply rooted in Kenyan society and many people are proud of their tribe.
Many Kenyans vote along ethnic lines, which meant that a dispute over allegations of fraud after the December 2007 election led to people being attacked and killed because they were from the same group as either the president or his main challenger.
Our correspondent says some people say they intend to answer "I am a Kenyan", when asked which group they belong to.
Collins Opiyo, from the National Bureau of Statistics, said it would have been "an exhibition of professional recklessness" to leave out questions about tribes.
"If we do not have the official position and people come up with figures and numbers we cannot be able to dispute them," he told the BBC's Network Africa programme.
The census is intended to shed light on a range of issues including education, fertility and mortality levels as well as migration patterns.
Security has been beefed up for the census, which will last all week.
Tuesday has been declared a public holiday as officials encourage people to answer the questions.